Electronic computing device



J. A. RAJCHMAN 2,428,81 l

v ELECTRONIC COMPUTING DEVICE I Filed oct. so, 1943 '12 sheets-sheet 1Oct. 14, 1947.

Oct. 14, 1947.4 J. A. RAJCHMAN 2,428,811

ELECTRONIC COMPUTING DEVICE Filed Oct. 30, 1945 12 Sheets-Sheet 2 WIUFJHi670? Hire/X VA wm N l u n# n" ew w w V6 7M 0 Z m.. #mw FW mw. a la m6 Nww 0 ma :Snventor X fan GM Gttorneg flo Oct. 14, 1947. l.1..fR/JGHMAIQ2,428,811

' ELECTRONIC couPuTIuG 'DEVICE Filed oct. 30. 194s 12 sheets-sheet 4 Azzz I -fam/ Suncntor A @Awe ria/:s af y wat mais any Bu www Oct.' 14,1947. J. A. RJCHMAN 2,428,811

ELECTRONIC COMPUTING DEVICE Filed oct'. so. 194s 12 sneetssneet s F/Ymy)X A F :inventor Gte-meu Oct. 14, 1947.

J. A. RAJCHMAN ELECTRONIC COMPUTING DEVICE Filed oct. s, 1943 12Sheets-Sheet 6 @rik U01 000| QWO) l Ol (Ittomeg J. A. RAJCHMAN 2,428,811

ELECTRONIC COMPUTING DEVICE Filed oct. so, 1943 Oct. 14, 1947.

PMs/crm# mme/x aufn/r Gttorneg Oct 14 .1947 J. A. RAJCHMAN y 2,428,811

ELECTRONIC COIPTING DEVICE lf'led Oct. 30, 1943y 12v Sheets-Sheet 9 15'Wfl/X F/X'f) FWS l 46H5 M/rf/rmmq sysrfn A M16 Snoentor lor#5.7024/7/02 Oct. 14, 1947. J. A. RAJCHMAN 2,428,811

IILECTROVNIGv COMPUTING DEVICE Filed Oc'c..l 30, 1943 12 Sheets-Sheet 10ffm?) M100 [Mw /4000 ma /00 '/0 l.

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P /Mw' mais INVENTOR a 'Mme/ @5M ATTORNEY 0t- 14 1947- J. A. RAJCHMAN iELECTRONc COMPUTING DEVICE l 12 sheets-sheet 11 Filed Oct. 30, -1943ugvErgToR www,

ATTORNEY Oct- 14 l947l J. A. RAJCHMAN 4ELEGTROHI COIPUTING DEVIGE Filedoct. so, 1943 12 shets-sneet 12 :inventor Jv: @jb/zgan Gttorileg Adigital position, signiies whether there is Patented Oct. l14, 1947 yELECTRONIC COMPUTING DEVICE Jan A. Raichman, Princeton, N. 1. assignortov Radio Corporation of America, a corporation 1 of DelawareApplication October 30, 1943, Serial No. 508,343 l (cl. zas-s1) 19Claims.

This invention relates to computing devices such-as are utilized togenerate a -desired function of one or more variables. The function andthe variables are represented by systems of electric potentials. It hasfor its principal object the provision of an improved computing deviceand method of operation whereby a function of one or more variables maybe derived continuously and without appreciable delay as the differentvariables change fromone value to another.

This improved computing device includes, among other elements, aselector matrix which operates to select a set of values of thedifferent variables, a function matrix which generates certain componentfunctions of this selected set of values, and an interpolator which socombines the various components as to present at its output terminalspotentials which are representative of the diflerent digits of a numberby which the value of the function is expressed. As will appear, each ofthese three elements may assume different forms, depending on theconditions under which the device is operated.

All the computations are performed in terms of numbers. The presentcomputing device is therefore of the numerical type, as contrasted withdevices using continuously variable physical quantities, such asvoltage, current or phase, as the variable of computation. The wholecomputation is made in the binary system of numeration so that anynumber is expressed as a sum of powers of two in which the coefilcientsof the terms are zero or one. 'I'hese are the only two digits of thebinary system. y

In this system, a number is expressed thus:

A=an2n+an12nr1+ ak2k| ao where the coeflicients ak are either one orzero. The numbers can be written in the usual digital representation asshown for'the first seventeen numbers in the following table:

For any number the iirst digit from the right, orzglrxt' a. 1 thenumber' or not, the second digital place whether there is a v2=21 or notthe third whether there is a 4=2 or not, the fourth whether there is an8=2 or not,l etc.

It is obvious that fractions and fractional numbers can beexpressed inthe binary system in a manner similar` to the decimal fractions by usinga binal-point" analogous to the decimal point. A table of a fewfractions would be:

0 .0000 1% .0001 1A; .0010 1% .0011 41 .0100 .0101 .0110 .0111 1/ .10001% .1001 .1010 H .1011 3/4 .1100 ii .1101 .1110 li f .1111

For any number the first digit from the right of the decimal pointsigniiies whether there is a. l/2=21 in the number or not, the secondwhether there is a 1/4,=2', the third whether there is a :24 or not,etc.

This system of numeration was chosen because most electroniccomputations are more easily performed in it than in any other system.This l unusual method of expressing numbers does not involve anypractical difficulty so long as the input and output of the computingdevice are `converted automatically to control somephysical apparatus,such as an'anti-aircraft fire control system. Under such conditions, nociphering or deciphering from the decimal numeration is involved. I

All the operation is made in a direct system in which the binary numberis expressed by a system of as many potentials as there are digits init, each potential having one of two definite values V1 and Vzcorresponding respectively to the digits zero and one. All thesepotentials exist simultaneously on a system of conductors each carryinga potential corresponding to one digit of the number. Thus, for example,to express the rst seventeen numbers, five conductors would be required.The number 9 would be expressed by the following excitation of the iiveconductors: V1VzV1V1V2,' since it can be written as 01001,

In a computing device, two or more such systems of potentials arecombined and a new system of potentials is derived from them. The resultof the computation is the stationary nal value of these outputpotentials. 'I'his result depends only on the stationary value of theinput potentials, regardless of the manner in which they were reached. Asudden change in one or continuous l v elements with inherently stablestates orany other holding devices, nor does it necessitate.

.y 3 A more input digits will, lafter short transients, cause the outputpotentials to reach their correct stationary values, so that theoperation of the direct computing device may be considered as It doesnot involve any trigger any definite sequence, timing, or clearingpulses.

erated is assumed to be continuous in the mathematical sense.'Such/functions are usually en'- countered when they relateV to physicalphenomena, as Afor example the ballistic func- Therefore, it is not acounter of any sort and does not involve impulses. Itis basically thefastest type of numerical device, since no time is wasted in the propersequencing of operations.

Important objects of the invention are the pro-,-

The invention will be better understood from the following descriptionconsidered in connec` tion with the accompanying drawings and its1 scopeis indicated by the appended claims.

Referring to the drawings:

Figs. 1 and 2 illustrate a function in graphical form, the curvedsurface representing the function in Fig. 1 and the curves of Fig. 2represent ing the function for various values of the y coordinate. ,f

Fig. 3 shows the -fu'nctionin tabular form with the variables in thebinary system.

Fig. 4 is a wiring diagram ofa selector whic operates yin response tomajor values of .the variables to select an element corresponding tothat particular set of values.

Fig. 5 illustrates a function generator which includes a modified formof selector, a function matrix and an interpolation system.

tions of a gun. 'The function may be in an'explicit mathematical formsuch as F(,:c, y) :V12-ky matical operations dening the function ratherthan to use the present device. However, most empirically foundfunctions are not susceptible of being expressed by simple mathematicalformulas. They are given in general in the terms of ta'bles or graphs.An example of an arbitrary" function determined in that manner is givenhere in graphical form (Figs. 1 and y2) and'in tabular form (Fig. 3). Y

Fig. 1 shows the function F0311) [plotted along v the coordinate z, as'afunction of the coordinates :z: and y in a rectangular systemfofcoordinates f as, il, e. Thus the surface z=F(:c, 11) may be consideredto represent the function. Two families of plane curvescan :be obtainedbyintersecting that surface by a series of v(ar-z) and y-z) planes. yTheselcurves are shown in perspective in Fig. 1. vThe curves (az-z) fordifferentvalues of y are also plotted in Fig. 2. The surface Z=F(, y)`or the curves Z=F(z)y=con$1;ant.

y represent the function completely for all points.

Figs. 6 and 'I illustrate details in the connecl tions of Fig. 5.

Fig. 8 illustrates an interpolation system which 3 differs from thatof.Fig. 5 in that it involves a single carryover system.

Fig. 9 illustrates a function generator adapted to the use of augmentedlinterpolating coefficients.

Fig. 10 illustrates the details of the interpolation system forming apart of the generator of Fig. 9, y

Fig; 11 illustrates an expanded scale section of the n function table ofFig. .3,

Fig. 12 is a :function generator adapted for use n of the scaleexpansion'illustrated by Fig. 11.

Figure 13 is a diagrammatic representation of an adding circuit,

Its

Any table, however large, cannot represent the function for all valuesof the variables since there is an innnite number of such values. Itmust therefore give the function for certain values only. yThe table ofFig. 3 gives the value of FCL', y) for 64 sets of values of m' and y.These particular values will be called the "major values and referred toas zo and yo. (The values of the functionl for these points` wereyobtained by measuring the Z values in Fig. 1.) The table is in the`binary numeration. The major values of the variable are chosen tocorrespond to exact yvalues of two, in this case simply thevintegers 1,10, 11, 100, 101, etc. In each square of the ta'ble, the irstnumbergiven is the value of the function. Thus, for the point Xn=100 andYo=11, the value of the function is found in square No. 29 to be011.1011. point Q of Fig. 1.

To nd the function for values of the variables` other than the majorvalues Xn and Yo, interpolation must be used on the basis of theknowledge that the function F(:c, y) has been assumed to be continuous.The simplest kind of interpolation is the so-called linearinterpolation, which is used in the iirst form ofthe invention.

It consists in replacing the actual surface Z=F(:v, y) by little planesfor each major area.

. corresponding to the interval between consecu- Figure 14 is a wiringdiagram of the circuit of Figure 13,

. Figure 15 is a diagrammatic representation of l amultiplying circuit,and i Figure 16 is a wiring diagram ofthe circuit of Figure 15.

The purpose of the present invention is to It will be explained for thecase of 3 generate arbitrary functions bythe direct method ofcomputation operative in the binary system. The device can operate togenerate funcp tions of one, two or any number of independent variables.l two variables :r and y as this case includes the complications due toseveral variables .without 1 ibeing unduly involved. 'I'he function tobe gentive major values of the variables, as shown, for example, by theheavily drawn area surrounding the point Pon Fig. 1, the region definedby. :en from to 101 and yo from 11 to 100. It is easy yto see, then,that the value of the function for any set of values 1.', y (representedby the point P) is given approximately by:

I A'.lo This relation is similar to the so-called Taylor series, inwhich only the rst order termsare taken into account. The values Aa: andAy, by which the actual values of the variable differ from the majorvalues, will ybe called the minor values. For the sake of simplicity, inthe pres# This is also represented by ent example they are thefractional parts of the variables. although in general it is notnecessary to make the separation between maior and minor parts justwhere the binal point is. 'I'he unit intervals Azo and Ayn, differencesbetween y consecutive major values, are thus equal to one.

Therefore the ratios AFz/Ao and AFu/Ayo, which are the rates of changeof the function with respect to .1: and y, respectively, are simplynumerically equal to AF and AFy. These valas can be seen on Fig. 1.

If the values of AFa: and AFy are known in ad- I dition-to the values ofF(:to, yt) for all major points, the value of the function for any otherpoint can be calculatedby the relation (I). This is precisely what isdone in the first forms of the invention. The table of Fig. 3 gives thevalues F(xu, yo), AFJ: and AFy for all the major values.

As an example, consider the point P of coordinates:

Therefore, the value of the function F(:r, y) `at P is:

F(.'E, y) =F(100.1101; 11.1110) =011.1011+ (.0011) (.1101)+(.1011)(.1110) :011.10114- .00101+.10011=100.0111 since (.0011) (.1101)- .00101and (.1011) (.11.10)-.10011.

As heretoforedndicated, the function generator Aincludes three principalelements or units, namely, the selector which selects a particular pointneighboring that at which the function is to be evaluated, the functionmatrix which makes available values of the function and desiredfunctions at that selected point, and the interpolator which combinesthese values with the differences of the variables at the desired andselected points, to produce the function inthe form of electricpotentials representing its various digits in the binary numeration.

The selector unit is disclosed in two diierent forms (Figs. 4 and 5). Inthe ilrst of these forms (that of Fig. 4), the major values :ro and yo,which are given in terms of binary numbers, are transformed separatelyto control an orthogonal network of function matrix input tubes. In thesecond of these forms (that of Fig. 5), the intermediary step ofseparate transformation of the major values :ro and yo is avoided. It isto be understood that the network is represented as orthogonal only forconvenience of explanation and that the two sets of conductors may haveany other convenient arrangement.

`The selector of Fig. 4 is shown as adapted for eight possible majorvalues of :to and the same number of mador values yo. There aretherefore 64 possible sets oi values, as indicated by the orthogonalnetwork 0i' tubes I to 64 whichare con- 6 nected in the input leads ofthe function matrix hereinafter described in connection with Fig. 5.

These values are established through three pairs of conductors 202 and203 for the yo input anda similar number of pairs 204. 205 and 206 forthe zo input. Each pair of these con--v ductors is connected at one endto some ofthe horizontal conductors (201 to 2I4 for the ya input and`others for the :ra input) oi the selector and at the other end to thecathodes of the selector matrix input `tubes 2li to 2I1 for the yo inputand 2I8 to 220 for the :ro input. Potential is appli/ed to the grids ofthe tubes 2I5 to 220 from leads maintained at -610 volts and -500 volts.as indicated in Fig. 4. The application of these potentials to the gridsmay be controlled by switches 22| to 226 as illustrated, or by anothercomputing device, or any other means which willmaintain these grids atpotentials corresponding to the binary numbers of the major inputs. Theselector output tubes 221 to 242 have been interposed between theselector input tubes 2I5 to 220 and the matrix input tubes I to 64.

It will be apparent that the switches 2I5'to 220 control the gridpotential of the selector matrix input tubes, i. e., set them at Vi=-610volts or Vz=500 volts. These tubes are merely amplifier tubes so that noappreciable power is drawn in the input circuit, and they are operatedas cathode followers.

It willbe apparent that the pairs of y" vertical conductors (left, Fig.4)

Vwill be excited according to the binary input potentials, i. e`., theleft conductor of any pair will be at -610 volts and the right one at500 volts for the digit 0 and vice versa for digit one. The horizontalconductors 201 to I4 are connected to the grids of the selector outputtubes 221 to 234 and are coupled through high resistances (1,000,- 000ohms) to the certain vertical conductors of the converter.

-The pattern of these couplings is as follows: Each horizontal conductoris coupled to the vertical wire which is at the most negative potential610 volts) of every pair for the particular combination of excitation ofthese vertical wires corresponding to its order number. For example, thegrid of tube 23| (binary 0II or 3 in decimal numeration) is connected tothe left wire of the pair corresponding to the digit 22 (|00), since itis at -610 volts when "0 is set on the switch |00, to the right wire ofthe pair corresponding to the digit 21 (I0), since it is at -610 voltswhen 1 is set on the switch I0, and finally to thev right wire of thepair corresponding to the digit 2 (I) since it is at -610 volts when 1is set on switch I.

It is apparent that the potential of the grid of any one of theseselector output tubes will be at -610 volts for the particularcombination of excitations of the inputs which correspond' to it, andwill be somewhat more-positive (at least by l 33 volts) for any othercombination of excitation since at least one of the vertical conductorsto which it is connected is at 500 volts. Therefore. one and only one ofthe selector output tubes will be cut oil, since the cathodes aremaintained at 600 volts, and it will be the one correspondwork is atrelatively high impedance since it is composed of 1,000,000. impedances.Further- 1 more, the cathode follower driving tends to keep c thecathode at approximately the grid potential Y l independently of theload. -The selector for the :ro variable is shown only diagrammticallyon Fig, 4; the coupling megohm resistances are heavy dots and theconverter output tubes 235 to t 242 arershown ascircles. This mode ofrepreis at the low impedance of 50,000 while the netcorresponding to themaior values or nro and ro together and to consider the resultingcombinafv tion as one single variable.

sentation will be usedV subsequently in order to simplify the drawings.

The anodes of the selector output tubes 221 to 234 and 235 to 242 arecoupled to the grids of the orthogonal network `function matrix inputvor double control grid tubes, and they are arof the table of Fig. 3. Toeach tube lthere correspondsa vertical exciting conductor comingconductor coming from the yconverter. If doutubes I to 6I. These tubescan eitherI be triodes c Therefore, a largerV converter from binary tonatural order (having 6 inputs and 64 outputs rather than 3, inputs anda 8 outputs) can replace both converters and the' orthogonal array oftubes of the iirst modifica-V tion. It operates quite-similarly to theconverters of Fig.` 4, except that the selected tube is made to conductrather than tobe cut ofi, as was thecase in the converters. To each ofthe digits (6 in the present example) of this new variable are assignedtwo potentials carried on two conductors 2li vto 206 which bear a push-por conjugate relation to one another, that is to say. for digit` zeroone conductor (the left one in Figs. and

` 6) is at the most positive potential V1 (-.i40y

1 ranged in an array corresponding to the squares L i from the:lr-converter and a horizontal exciting -ble grid tubes are used, asshown for tube 53 on Fig. 4, the vertical wire is connected directly toone grid andthe horizontal to the other. It 1 will be apparent that onlyone out of the 6I tubes of the array will conduct, the one for whichboth grids are at -340 volts, e., when the corre-l t sponding tube ofthe zo converter is cut olf (plate t l at 340 volts) and-thecorresponding tube of the y converter is cut ofi. For all other tubes,one or the other or both of the grids will be more negative than 340volts, say at 500 volts. so that they will be cut off,

If triodes are used, as shown for tube 29 in Fig.

l' 4, the single grid of the triode is coupled through a 1,000,000 ohmsresistance to the horizontal con.- duotor and through another 1,000,000ohms to 1 the vertical conductor. It is apparent again that only theparticular triade lying in the intersection volts) andthe other (theright one on Figs. 5 and 6) is at the most negative potential V2 (-600volts) and for digit one the potentials of the two i conductors areinterchanged.

o The selector matrix is composedof two sets of orthogonal conductorsbetween which high coupling .resistances (2.700,000 in the presentexample) are connectedV according toa predetermined pattern. On Fig. 5the heavy dots on the selector matrix (left)A represent suchresistances, which are to be understood as connected between the twoconductors on the intersection of which they are drawn. The verticalconductors carry Y the input potentials andthe horizontal wires are ofthe excited conductors will be conducting.` The i grid of thatparticular triode will be at -340 3 volts, whereas all other' grids willbe mor negative by at least half the potential variation of theconverter output tubes,and will therefore be cut off since the cathodesof all the triodes are at 340 volts. It may be noted here, as it was inthe case of the converter resistive networks, that i the resistivenetwork of the plate of the coni verters to the grid of the functionmatrix input tubes has many parasitic connections producing Y extraneousexcitations, Here again the operat l tion is as stated in spite ofthese' because the driving impedances are low (20,000o) and the icoupling resistances are high (1,000,000o).

Whether triodes or double grid tubes are used Therefore, it will ya, oneparticular horizontal `lead of thev function -mat will be excited. Theseleads are shown on the right of Fig. 4, or extending above i the tubesito 6I.

The same result can be obtained with a simple selector built accordingto the second modiiication. Such a selector is shown at the left of Fig.5, while Fig. 6 shows the detail of thecircuit.

t The basic idea is to combine the input potentials connected to thegrid of the triodes (halves of 6SN7s in the example of Fis. 6) of thematrix input tubes (shown as numbered circles in Figs. 5 and 6).The'push-pull signals are obtained from a, previous computing device, orthey may be set in by a series of switches. input tubes 2I5 to 220(lower left, Figs. 5 and 6) are merely ampliiers, so that no appreciablepower is `drawn in the input circuit and they operate as cathodefollowers, as did the input tubes to the converters of Fig. 4. Y

The pattern of resistances is determined as fcllows: Any one ofthe-horizontal conductors of the selector matrix which is connected tothe grid of a triode of the input matrix tubes (numbered I to 6l on Fig.5) is coupled through' high (2,700,000o) resistances to the verticalwires Y whichfare at the most positive (Vz=-340 volts) of the twopotentials V1 and V: for th'eparticular combination of excitationcorresponding to that f selected triode. It is thus obvious that thishorizontal grid lead will beat the positive potential Vn 340fvolts) forthe combination .of excitations corresponding toit and will be at somepov tential negative with respect to V2 forany other combination.

This results from the fact that for anyother combination'at least yoneof the vertical conductors to which that particular triode-grid iscoupled will be at the more negative potential V2=600 Volts, S0 thatthere Will be (l-1) [in the present case o -1=5] connections at V2(=-600 volts) and one at V1 (=340 volts) and the potential assumed bythe lead will `be rthe -(5.340+600) [iig- 383V volts] which is negativewith respect 'to V2.

odes, only the tube corresponding to the selected? value represented bythe input potentials will conduct and all others will b e cut oi. As an.A example, consider the connection to tube No. 29

for which 10:10() and 210:011; therefore, the new variable has the value100011, so that the pattern The selector Therefore, with the proper bias340 volts in the present case) on, the tri of resistances for that leadis RLLLRR, as can be seen on Figs. 5 and 6.

The remark concerning parasitic connections made in connection with theselectors of Fig. 4 applies as well to the selector matrix of Fig. 5.The possible undesirable extraneous excitations do not interfere withthe proper operation because the coupling resistances are high (2,700,-000 ohms), the driving resistances low (50,000w) and the driving circuitisV degenerative (cathode follower).

The purpose of the selector described above is to "select a point :to-yowhich corresponds to selecting a certain vsquare on the table of Fig. 3.The purpose of the function matrix is to assign to this square thevalues of the functions F(zo, y), AF2: and AFy which are'indicated bythe table,

The function matrix is represented diagrammatically on Fig. 5 (upperright). The details of the connections are shown on Fig. 6. The matrixis illustrated as composed of two systems of orthogonal conductors, theorthogonal relation being a consideration of convenience and not of,

necessity. The horizontal conductors are connected to the plates of thefunction matrix input tubes (I to 64 of Fig. 5) which are both thevoutput tubes of the selector matrix and the input tubes of the functionmatrix, and the vertical conductors are connected `to the-grids of thefunction matrix output tubes 243. The state of excitation of thesematrix output tubes represents the three functions to be generated. Onesuch tube is assigned to each binary place of the functions. In theexample used here, there are three sets of output tubes, the rst forF(o, yo) having seven tubes to take care of the seven places or digitsencountered for that function in the table vof Fig. 3,*the second andthird each having nine tubes to take care of all significant placesencountered in the functions AF and AFy in the table of Fig. 3.

The vertical wires are coupled to thehorizontal wires through highcoupling resistances (R=l, 000,000 ohms) according to a predeterminedpattern, i. e., certain vertical wires areY coupled to certainhorizontal ones, the choice of the wires or the patternl determining thefunctions to be generated. A resistance is connected between a givenvertical wire corresponding to a given set y of major values aro-yo Aanda given horizontal wire corresponding to a. given binary place of thefunctions when the vdigit of that binary place happens to /be one. Theresistance is omitted if that digit happensto-be zero. The function isthus recorded in terms of existing or non-existing resistances. As anVexample, consider the square 29 of Fig. 3, and the corresponding inputmatrix triode No. 29 on Figs, 5 and 6. The values of the three functionsare F0120, 11o) :011.1011 AF$=00000.0011

and

Therefore, the potential of the selected horizontal wire becomesnegative (in the present case about -200 volts, assuming a current of 10ma. in the tube No. 29, since the +B is'at 0.5 volt, see Fig. 6). Thiscauses the potential ofi the vertical wires to which this selectedhorizontal wire iS coupled to Ibecome more negative than the ones towhich that wire is not coupled. Therefore, with proper bias (zero in thecase of Fig. 6) of the output matrix tubes, the tubes which are coupledwill be cut off and the ones which are not coupled will be conducting.Therefore', it follows that the output matrix tubes will beexcitedaccording to the predetermined function set in thev functionmatrix of resistances.

The detail of the connections of the matrix output tube is shown on thelower right portion of Fig. 6.. Consider a typical output tube 243, forexample, the one on the lead marked .001 (right) This tube is a pentode6SJ7.` A neon lamp 244 is inserted in the plate circuit to provide avisible indication of the state of conduction of the tube. This, ofcourse.- is not essential since the functions F(x, yo), AF2: and AFy areto be combined according to .the relation of Equation 1 before the finalresult F(:c, y) is obtained.- The reason for the different circuit shownfor the tube connected to the lead I0 is explained below.

In the function matrix of resistances every ver- 'tical conductor isconnected to all horizontal conductors and vice-versa. In fact, there isa connection between any two conductors. Therefore, when the inputconductors are excited they produce not only the desired excitation onthe desired, outputl leads, but also parasitic excitations on otherleads. The matrix is therefore designed in such-a manner as to reducethese parasitic effects to such an extent as to make the ratio of'(9-1-9-|-7=25 in the present case); i the current.

through the driving triodes l to 64 (10 ma, in the present case); Rbtheir plate resistance (20,000 ohms), Rc the coupling resistance(1,000,000 ohms in the present case) Es the true signal and Ep theparasitic signal on the grids of the output tubes. 'I'hen assuming theworst possible conditions, i. e., the weakest true and largest falsesignal, the following relations. hold:

Effe-1") Therefore the attenuation, i. e., the ratio of driving signalon triodes to useful signal, depends only on the number N of inputelements. In this case N=64 so that the weakest useful'signal on thegrid of the output'pentodesv is about volts which is sufficient to cutoff the tubes 243. The4 ratio of. true to false signals depends onlyAexcept a particular one.

11 1 on the ratio of plates to coupling resistances and the number ofoutputdeads `p. In the present case this ratio is 1,000,000 I'(zumo-)mp3 assumed worst case when all .the horizontal leads areconnected to a given vertical lead. 'Ihis case may well occur. In spiteof this the attenuation factor may be reduced to N/2 by the followingexpedient. The number of coupling resistances' for any one vertical leadmay be smaller or greater than N/2. If it is smaller, the attenuation ofthe signal for that particular signal will be less than N/Z. If it islarger, that means that there are Aatraen the compensating resistances?are different for everyy conductor.

In many applications it is desirable many functions ofthe samevariables, as is the case, for example, in anti-aircraft nre computers.

' Itis also the case for a single function if a method f can obviouslybegenerated by the same device.

more digits one than digits "zero for that particular verticalconductor. The expedient consists in that case in using a couplingresistance at every place which corresponds to the digit `zero(in-st'ead of one) and omitting it for places correls'ponding' to thedigit one (instead of zero). In

this manner the number of resistances on every vertical wire is less (orequal to) than N/Z (32 in the present case) ,so that the maximumlattenuation is N/2. Of course. this expedient requires that thepolarity of the signal on the'wires where the resistances have beenpermuted be reversed. This is shown for the line marked I0 in the lowerright part of Fig. 6. An additional phase inverting tube 245 (6SN'7)y isused for the purpose. It

.can be seen that the true signal on the matrix output tubes is now200/32-6 volts (instead of 3 volts).

'I'he relations (3) andj. (4) mentioned above have been established forthe case of maximum attenuation, i.` e., one vertical lead is connectedto all horizontal leads (and the corresponding digit is always one) andmaximum parasitic signal, when all the matrix is full of resistances Inpractice, the matrix will be filled in some random mannerso that theuseful and parasitic signals will be different for each output conductorand different for every excitation. It could happen therefore that theratio of the weakest useful signal at some particular conductor to thestrongest parasitic signal at some other conductor would not be as greatas indicated by relation (4). To bring all conductors to a standardcondition of attenuation equal to N/2 the vertical leads are coupled tothe plate supply of the input tubes (+0.5 volt in our example) throughcompensating resistances Rd which are adjusted for each conductor so asto make the loading uniform. (See Fig. 6.) For example, the value of theresistance for lead marked |00 is` 200,000 ohms. This value wasobtainedby considering that the maximum number of' coupling resistanceson any one vertical lead is 32, and that the number of resistances onthat lead is 27,: therefore, a loading corresponding to five couplingresistances in parallel' is necessary to bring that lead to the 32loading, standard condition.V

Therefore the corresponding compensating resistance is1,000,000/5=200,000 ohms. Qi goutte,

of interpolation more refined than linear is used.;`

Any number of functions of the same variables It suffices merely toconnect their "function" matrices to theflrst function matrix. Itamounts l to increasing the numberp of vertical conductors. This can bedone without further changes in the device as long` asthe parasiticsignal does not become unduly large. However. it is seen from relation(4) that asp increases, the ratio of true to false signal tends towardunity. By using a large Rc/Rb ratio the number of usable places can befairly large. There is a method by which there is no limitto the numberof functions which can be generated. It consists of using a degenerativedrive of the matrix, using two tubes instead of one for every inputplace of the matrix.

Fig. 'I shows one typical driving arrangement for'any input (horizontal)conductor. The output of the selector and input of one function matrixare two separate tubes (rather than'a' single one). The output of theselector is con' nected as before. 'I'he input of the function matrix isderived from the cathode rather than the plate. The tube 241 isconnected as a cathode follower so that the potential of the cathode is`approximately equal to that of the grid regardless` of the load. Thismeans, therefore, that, the

parasitic signals will be suppressed all together since the potential ofall the non-excited horizontal leads of the function matrix will beforcibly maintained at +0.5 volt, in spite of parasitic effects whileonly the excited lead will become negative.

The function table as described has two matrices of resistance, theselector matrix, which determines which values of the major parts of thevariables .are assigned to which values of the function, and thefunction matrix, which deter--v mines the nature ofthe function. vBothof these are arbitrary, that is to say, the pattern o f.

resistances can be chosen t'o express any desired function.

A particularly convenient method of mounting the large number ofresistances consists in holding them in holes drilled in a-,Bakeliteboard.

The board is drilled according to the desired pattern and theresistances are inserted and soldered in piace with the two sets ofconductors on opposite sides of the board. If the generator is`installed in someV computing device whereit is desirable to change.frequently the nature of the function, as may be the case in computersfor re control when types ofv guns or shells are changed, the board ofresistances may be provided with jacks and may be plugged in and outwith-y out disturbing any permanent connections.

When the function F620, iin) and the interpolating coeilicients AFa: andAFV are known, it sumces to make the two multiplications and the twoadditions indicated in relation i) to obtain the de-v sired function F(,y). Means for doing this are shown diagrammatically on Fig. 5. Thesquares 256 and 4201 symboli multiplying and adding devices operating bythe direct method. 'I'he upper sides are the terms ofthe product, the

lower right side the result.

to generatel In a first form, the adding and multiplying device issimply the one tube device such as is disclosed in the aforesaidcopending application serial No. 496,746. The inputs to the-e1ectroniccalculating tube are direct without any coupling tmpedances, asexplained in that application. Of course, it must be kept in mind thatthe different inputs must be on the same D.C. level, which means thatthe minor parts of vthe variables Aa: and .Ay must be brought to thesame level as the interpolating coefiicients 'AF and AFy.

In a second form, the adding and multiplying devices are the directmultiplier and adder described in my copending application Serial No.511,729, lled Nov. 25, 1943. As previously mentioned, the variousmultiplications and additions required to combine the major values x'and yo, the minor values Aa: and Ay'and the interpolating coefficientsAFa: and AFy, as indicated by the squares and legends at the lowerright-hand corners of Figures 5, 9 and v12, may be performed by devicesof the type disclosed by myl copending application Ser. No. 496,746.Thus in the case of the square 256 of Figure 5, for example, the AF.:leads are connected to the multiplicand leads of Figure of the copendingapplication, the Am and vForo, ya) leads are connected respectively tothe multiplier and the input B leads and potentials representative oi'the value of Az,

are produced at the output leads bearing the numerals 25, 26, 2'I and28. The square of Figure 5 indicated the numeral 251 is a second devicewhich is similar to that of the copending application and functions toderive the'product Ay, AFy and to add this product to the output Az,AF+F(xo, yo) of the device 256. 1

The various additions involved in deriving the value of the functionalso may be performed by the adding circuit which is disclosed in mycopending application Ser. No. 519,299 (Patent No. 2,404,250) and wasmade prior to the iiling date of the present application.

This adding circuit is disclosed in Figures 12 and 13 of the presentapplication.

Figure 13 is a diagrammatic representation of a computing circuitarranged in accordance with the invention for adding two numbers (A andB), of six digital positions, circles being used to indi- 1 cate theelectron discharge devices involved in the various connections. Y

The circuit of Figure 13 includes one group of input tubes 3|0 to 3|5 towhich are applied potentials representative of the various digits of anumber A and another group of input tubes 3|6 to 32| to which areapplied potentials representative of the various digits of a number B.In each of these groups, the lowest digital position is at the top andhighest digital position is at the bottom. This is indicated by thebinary numbers placed above the various input leads. When -180 volts areapplied -to an input lead. the digital position which it representscontains a zero. When zero voltage is applied to one of these inputleads, the digital position which it represents contains a one. Switches340 and 34| Y ard amount for each tube that is made to conduct thestandard units of 4 ma. a'nd each of the tubes may be considered asrepresenting a digit one or a digit zero.

For converting these various digits into a ybinary number which is thesum of the two num'- bers, a group of carryover tubes 322 to 326 and agroup ofl carry over control tubes 321 to 332 are (Fig. 14), anothercomputing circuit or any other digits oi' the two` numbers to beadded.Each of provided. The resulting sum is indicated by a group ofindicators 333 to 339 which may include a, neon lamp or the like. Themanner in which these results are accomplished will be more easilyunderstood-in connection with Figure 14.

Figure 14 shows the details of that part of the. circuit which appearsin the heavy lines of Figure 13. It will be noted that the input tubes3|3 and 3|9 are connected to the same terminal of the resistor 342 asthe carry over tube 325 which has its control grid connected to thecarry over control tube 332 for applying a positive potential when a oneis to be transferred from the second digital position to the thirddigital position which is representedby the input tubes 3|3and 3l'9. Allthe carry over tubes 322 to 326, like the input tubes 3|!! to 32|, areof the cathode follower type so connected as to conduct a standard unit'(4 ma.) of current. y

It is apparent that the potential at the lower terminal of the resistor342 is reduced by a. predetermined amount when one of the tubes 325, 3|3or 3|9 takescurrent, by twice this amount when two of these tubes takecurrent and by three times this amount when all three of these tubestake current. These different voltages are applied through the resistors343 and 344 to the first or control grids of the indicator tube 331 andthe carry over control tube 330. Potential is applied also to thesegrids from a v. lead through resistors l'345 and 346. o the second orscreen grids of the tubes 330 and 331, potentia1 is a'pplied from a +45v. lead. l

Connected in shunt to the tube 331 'is a neon tube 341 for indicatingwhen this tube is not conducting (a condition existing when a digit zerois lin the third digital position of the sum of the two numbers beingadded). l

The carryover tube 324 of the fourth digital position has the upper endof its cathode resistor connected through a resistor 348 to the first orcontrol grid of the indicator tube 331. The control grid of the tube 324is connected to the diode element of the tube 330 and through a resistor349 to the anode of the tube 330 so that the tube 324 conducts currentonly when the tube 330 is biased off. The purpose of the diode -elementof the tube 330 is to establish at the grid of the carry over tube 324 apredetermined potential which is intermediate those of the +550 v. and'-600 v. leads when the tube 330 becomes nonconducting and no platecurrent is drawn through its anode resistor by the tube.

The manner in which the circuit operates to convert the digitsestablished by the tubes 325,

.From uns tabulation, it is @violent that the and 3I9 is conducting;When one of the tubes 325, 3| 3- or 3 I3 is conducting, thepotential-atthe lower end of the resistor 342 is reduced suiliciently tobias oif the tube 331 thereby lighting the lamp 341 and indicating adigit one in the third digital Aposition of the binary number. When twoof the tubes 325, 3I3 or 3|9 are conducting, the potential at the lowerend oi.' the resistor 342 is re- I tubes 330 and 331 are conducting andthe tube 324 is biased oil when none of the tubes 325, 3|3` ducedsufficiently to bias oil the tube 330. This has two results. It makesthe tube 324 conducting so that a. digit one is carried over to thefourth digital position. When the tube 324 conducts, a

coincidence effect is utilized to produce the terms AaBx. However.additions of intensities are utilized foi` the summations. although thiscould beaccomplished in other ways.

,The two systemsof potentials representing ranged, as shown in Figure15, in an orthogonal network whose intersections constitute the ele--ments of a. matrix corresponding to the terms AxBr. A vacuum tube 436on each of these intersections is made to conduct only if there iscoincidence of excitation of the two wires at such iny tersection, andtherefore give a value to Aix only when A1 and Bx are both one. All thecoefilcients A1Bk corresponding to the power 2l+k are located ondiagonal lines,l vertical on the Figure 15.

Therefore, if all the plate currents of the tubes on these lines areadded, the total current will be proportional to the coeiilcient of the21+k term, provided that each tube, when conducting, contributes astandard amount of current. 'The system of potentials assumed by theplates is already a representation of the product, but it is not in thebinary"system, vsince the c'oeillcient'of each positive potential isapplied to the control grid of the tube 331 so that this tube takescurrent and thelamp 341 is extinguished. When all of the tubes 325, 3| 3and 3|! conduct the potential at the lower end of the resistor issufilcently negative to bias oil both tubes 333 and 331 so that thecarry over tube 324'remains conducting and the lamp 341 is lighted.Under these conditions, a binary number of 1100 is established in thepart of the circuit detailed in Figure 14. How the complete sum of twonumbers represented by potential applied to all the input leads isestablished is readily` understood from the foregoing explanation. Howthe carry over system of Figures 13 and 14 is extended to produce thesum of numbers having a higher number of digits will be understoodreadily from consideration ofthe multiplying circuit of Figures 15 and16, since this multiplying circuit employs the samecarry over andindicating system as that of the adding circuit. y

'Ihe multiplying circuit of Figures 15 and `16 may be utilized toperform the various multiplications required to produce thevselectedvalueof the function. By this multiplying circuit, the product of twobinary numbers is obtained in the form of potentials representative ofthe digits of such product.

The product of two binary numbers :c and y power of 2 may be larger thanone. To obtain the answer-in the binary system, the Si current stepsappearing in the i row of each 2p+2frows must be revalued into binarynumber places to excitethe proper carry-over and indicating` tubes. Thiscan -be done in several different-ways.

It has been found that the -most convenient manner is as follows: Let

Si=Ci+2Di+1 .YL 2"DH It is apparent that if there are m carry-over tubeslocated on the rows (j+1), f

(J+2) (v+m) which are excited when the corresponding coef-r ilcient D isone, the proper carry overs will be obtained provided that the circuitof each carryover tube, added to the circuits of the proper row, willcontribute the same standard amount of current as the tubes of thematrix. 'I'his is so bethe 2p+2 rows which win be excited when-'thowhere A1 and Bk are equal to one or zero, can be scales the number ofanswers in the basic multiplication table of digits is always greaterthan the n radex. In accordancewith this invention. that of theorthogonal network because the current cause any one of the coeillcientsDHA multiplies the power 2H* and is added .precisely tothe rowcorresponding to the (i4-Mm power, as herein-k after explained indetail. To'obtam thoresulafit suffices merely to provide an indicator oneach of corresponding coeillcient C; is equal to'one. The carry-overtubes 455 and 483 and indicator tubes 484 to 495 for the case of p=5 areshown on Figure 15. 'lhe thirty-six tubes 435 of the matrix and thecarry-over tubes 455 to 483 all contribute a standard current whenconducting. The tubes 436 contribute no currentwhen there is noexcitation from one of the corresponding leads. Auxiliary amplifyingtubes 496 to 5I3 are used in one modification of the invention.

'I'he basic part oi'- the multiplier is the circuit which will producethe signals to excite the indicator and carry-over tubes, according toEquation, 4. This circuit is repeated on each one of the (2p+2) rows,with various degrees of comwill .be readily understood from a fewexamples.

There can, of course, be no carry-over from the tube 435 at the lowercorner (diagonal No. l)

I. and y are carried by two systems of wires ,ar-

